UKH

I'm looking to replace my old road bike/ commuter. Looking on the cheap end of the market as it is more of a commuter than actual road biking. The one I am replacing was my first ever road bike, and I have liked it but have nothing really to compare it to. Looking at a replacement now, and there is someone selling a BTWIN (Go outdoors) bike second hand that looks like it is in reasonable nick and is dead cheap. 

My hesitation is that it has 650 wheels rather than 700. Would I notice the difference when I am road riding with it? (Obviously makes no difference for the commute). What are the pros and cons of each size of wheel?

Might suit a smaller frame if you’re a smaller person perhaps. Lower gearing compared to 700.  Poss bit lighter. Beyond those guesses not sure. GCN videos might help. 

Smaller wheels on a small frame mean you are less likely to get toe-overlap which is always nice

A bit harder to get spares in a pinch as 650b is a little less common, so you range of choice will be more limited compared to 700c. A decent bike shop should have what you need.

650b wheels make for a slightly more agile or twitchy feeling (you probably won't notice)

Main issue with 650C is the limited choice of tyres or replacement wheels. If anything you might actually find you prefer 650 over 700 as 700s can be quite out of proportion in a small frame (assuming you're probably 5'4" or less to be looking at frames which use 650C). You may find the bike sits lower to the ground and has greater clearance from your toes which are both good things for handling.

Btwin are decathlon bikes. I recently bought a btwin triban 540 to replace a trek destroyed by a inatentive driver along with my leg and so far I've been pretty happy with it. The frame is a bit agricultural but is strong and has bosses for guards and panniers (so good for commuting) and the finishing equipment is excellent for the price. If anything it looks too nice for leaving outside work.

Yes, decathlon! I had looked at what go outdoors had too, so got them muddled! Lol.

Yes, it does look quite well kitted out for a cheap bike.

I went to see it last night, and it feels quite different to the bike I was using but it's hard to tell on a short trial spin what that will feel like over a longer distance. It feels much smaller than my previous one despite being the same frame size, so I presume that is one of the differences of the smaller wheels. 

I decided to take it as it was cheap as chips, so if I don't like it over longer distances then I can just use it as a commuter and look for something else for road riding