Comparison of values in dictionary
Index less

Also, you're indexing a lot. Perhaps it's better to seperate the two dicts:

old, new = results_dict["Current model"], results_dict["New model"]


(And what's up with having an underscore in Current_model and a space in New model? That's asking for typos. You're not even consistent with it - in your first code they're both spaces, but in the assignment you use 3 underscores and a space for Current...)

Also, with how you make the checks, one of your conditions always implies the other. You should remove the redundant comparisons. Change:

if recall_new &gt; recall_current or recall_new &gt; (recall_current-(0.1)):
# Into:
if recall_new &gt; recall_current - 0.1:


The additional braces don't do anything, and if recall_new is bigger than current-0.1, then it is also bigger than current. 

Loop

If you look closely, you'll see you're doing the same thing multiple times. So just make it a loop.

Arguably you should make an outside variable for the keys to iterate over, or iterate over the keys of either new or old dict. But if hard-coding is appropriate, it could look a lot like:

new_better = 0  # i is a bad variable name. Names should have meaning.
for key in ("Recall", "Precision", "F1_score"):
    if new[key] &gt; old[key]-0.1:
        new_better += 1
if new["Frauds"] &gt; old["Frauds"]*1.2:
    new_better += 1


Note that I removed your rounding. Python has no issues transforming a float to the closest integer by means of int(), but neither does it have a problem with comparing ints to floats. I did notice that your adjustments make it easier to score an increment for the first three variables, but harder for the fourth. Is this intentional?