Completely different feel and an entire price segment of difference between them. The Forester is closer (particularly the upcoming 2019 Forester) and might make for a better compare/contrast. However,
The Ascent is a big vehicle and it feels like it when you're inside. It doesn't drive as big as it feels though...but sitting in each vehicle, the dichotomy is very evident. It has considerably more 'feeling of acceleration' with a WOT. It is more refined and comfortable inside than the Crosstrek.
The Crosstrek is a lifted Impreza Hatchback (and that would be a more fair comparison). It has a more 'adventurous' feeling interior, lacks bottom (and top) end power (I think the crosstrek is nearly perfect though, the lack of power isn't a downside to that car). A loaded Crosstrek Touring still cannot touch the MSRP on an Ascent Base with no options. The Outback and Forester fill the gap on the low side of things. The Crosstrek is more nimble (and, anecdotally, probably more capable out on the trails due to its size, but I could very well be incorrect on that).
The Ascent is a people mover. As such, it is full of comforts (42 USB ports, 952 cup holders, sun shades, ventilated seats, etc). The Crosstrek is an adventure vehicle. It really was genius on Subaru's part. They took an Impreza, lifted it, kept the same price range as the Impreza, and made a new vehicle out of it. It has just enough features to appease most people, but is considerably less comfortable (in an overall sense, not talking about the seats) than the Ascent. There's much less room, no Touring option, etc. My only wish for the Crosstrek is to have it in Limited trim with a manual transmission. I'll purchase the first one we get off a truck if that ever happens.