Aero bike vs climbing bike for running in Crits
Revised following clarifying comments


OP is / will be racing in the US 
USA Cycling has looser rules for bikes than the UCI, unless the event is qualification for a non-US event.


With these updates, the answer is simply that people rarely race on ideal equipment. Most people I know who race Crits do it either on the same bike they use for road races, Gran Fondos, or other big rides, because they don't have a more suitable bike for the purpose. Those who can afford to drop $5K to $10K on a specialist bike usually don't see Crits as the target: too many crashes, and they tend to see Crits as training rides.

Regarding the bikes you mention, they both appear on a quick glance to meet the USA Cycling Rules 2017. I was initially concerned that the curved top tube was non-compliant, but this guide and the rules already mentioned show that concern to be unfounded for racing in the US. I suspect the FM098 would not meet UCI standards, but that's irrelevant to you.

The earlier version of this answer follows and may be useful for international readers ...



ARTICLE 1.3.011 (and related articles) of the UCI Technical regulations essentially says only a general purpose bike can be used for road racing (criteriums are road races).

I interpret your aero bike to be a time trial bike. The rules explicitly ban such trials bikes from road racing. 

The reason for this is the lack of maneuverability. 

In practice you'll get much more benefit from sitting on the guy on front. 

See UCI CYCLING REGULATIONS PART 1 GENERAL ORGANISATION OF CYCLING AS A SPORT  

Especially 1.3.022 and 1.3.023.