Personal perspective as a Harpenden resident.
If I had unlimited funds, I'd live in the Avenues - it's close to town, close to the Rothamstead Park and has some very lovely properties. West Common is often a car ride to the station, the station car park gets incredibly busy, so if you're driving you have to get there early, being within walking distance of the station is very handy if you like late starts. West Common also feels a little more conservative, a bit dull, a bit wealthy & retired - that's personal opinion. Both are regarded locally as high status areas.
Neither location is particularly good when it comes to state schools - West Common has had problems in the past accessing Harpenden Secondaries being that bit further away...the Avenues is closest to St Nicks and St Dominics but they are faith schools and unless you are a church goer forget getting anywhere near them, you don't have a hope!
For standard state primary, neither location is very close but given the prices you pay for either location, funding independent primary schooling shouldn't be a problem.
I wouldn't be too concerned about either location though, they are both very lovely. We moved from London a few years ago and we love it here. Hope you find a property you like, there never seems to be much on the market.