Performance of an In-Memory Table is worse than a disk-based table
While this post won't be a complete answer due to lacking information, it should be able to point you in the proper direction or otherwise gain insight which you can later share with the community.


  Unfortunately, this definition results in a degradation of performance with respect to the previous situation with a disk-based table. The order of magnitude is more or less 10% higher (that in some cases reach 100%, so double time).
  
  Most of all, I was expecting to gain a super-advantage in high-concurrency scenarios, given the lock-free architecture advertised by Microsoft. Instead, the worst performances are exactly when there are several concurrent users running several queries on the table.


This is troubling as it should definitely not be the case. Certain workloads are not for in memory tables (SQL 2014) and some workloads lend themselves to it. In most situations there can be a minimal bump in performance just by migrating and choosing the proper indexes.

Originally I was thinking very narrow about your questions regarding this:


  Questions:
  
  
  what is the correct BUCKET_COUNT to set?
  what kind of index should I use?
  why the performance are worse than with the disk-based table?
  


Initially I believed there to be an issue with the actual in memory table and indexes not being optimal. While there are some issues with the memory optimized hash index definition I believe the real issue to be with the queries used.

-- INSERT (can vary from 10s to 10,000s of records):
INSERT INTO MyTable
  SELECT @fixedValue, id2, col1, col2 FROM AnotherTable


This insert should be extremely fast if it were only involving the in memory table. It, however, also involves a disk based table and is subject to all of the locking and blocking associated with that. Thus, the real time waste here is on the disk based table.

When I did a quick test against 100,000 row insert from the disk based table after loading the data into memory - it was sub-second response times. However, most of your data is only kept for a very short amount of time, less than 20 seconds. This doesn't give it much time to really live in cache. Additionally I'm unsure how large AnotherTable really is and don't know if the values are being read off of disk or not. We have to rely on you for these answers.

With the Select query:

SELECT id2, col1
FROM MyTable INNER JOIN OtherTbl ON MyTable.id2 = OtherTbl.pk
WHERE id1 = @value
ORDER BY col1


Again, we're at the mercy of the interop + disk based table performance. Additionally, sorts are not cheap on HASH indexes and a nonclustered index should be used. This is called out in the Index guide I linked in the comments.

To give some actual research based facts, I loaded the SearchItems in memory table with 10 million rows and AnotherTable with 100,000 as I did not know the actual size or statistics of it. I then used the select query above to execute. Additionally I created an extended events session on wait_completed and put it into a ring buffer. It was cleaned after each run. I also ran DBCC DROPCLEANBUFFERS to simulate an environment where all of the data may not be memory resident.

The results weren't anything spectacular when looking at them in a vacuum. Since the laptop I'm testing this on is using a higher grade SSD, I artificially turned the disk based performance down for the VM I am using.

The results came in with no wait info after 5 runs of the query on just the in-memory based table (removing the join and no sub-queries). This is pretty much as expected.

When using the original query, however, I did have waits. In this case it was PAGEIOLATCH_SH which makes sense as the data is being read off disk. Since I am the only user in this system and didn't spend time to create a massive test environment for inserts, updates, deletes against the joined table I didn't expect any locking or blocking to come into effect.

In this case, once again, the significant portion of time was spent on the disk based table.

Finally the delete query. Finding the rows based off just ID1 is not extremely efficient with a has index. While it is true that equality predicates are what hash indexes are proper for, the bucket that the data falls into is based off the entire hashed columns. Thus id1, id2 where id1 = 1, id2 = 2, and id1 = 1, id2 = 3 will hash into different buckets as the hash will be across (1,2) and (1,3). This won't be a simple B-Tree range scan as hash indexes are not structured the same way. I would then expect this to not be the ideal index for this operation, however I wouldn't expect it to take orders of magnitude longer as experienced. I would be interested in seeing the wait_info on this.


  Most of all, I was expecting to gain a super-advantage in high-concurrency scenarios, given the lock-free architecture advertised by Microsoft. Instead, the worst performances are exactly when there are several concurrent users running several queries on the table.


While it's true that locks are used for logical consistency, the operations must still be atomic. This is done through a special CPU based compare operator (which is why In-Memory only works with certain [albeit almost all cpus made in the last 4 years] processors). Thus we don't get everything for free, there will still be some time to complete these operations.

Another point to bring up is the fact that in almost all of the queries, the interface used is T-SQL (and not natively compiled SPROCs) which all touch at least one disk based table. This is why I believe, in the end, we aren't actually having any increased performance as we're still constrained to the performance of the disk based tables.

Follow-Up:


Create an extended event session for wait_completed and specify a SPID known to you. Run the query and give us the output or consume it internally.
Give us an update on the output from #1.
There is no magic number for determining bucket count for hash indexes. Basically as long as the buckets don't get completely full and the row chains stay below 3 or 4, the performance should stay acceptable. This is kind of like asking, "What should I set my log file to?" - it's going to depend per process, per database, per usage type.