Well I've not stayed in either of them but I've just taken a look at their locations, so I'll try to help anyway.
The Melià Barcelona Sky (which is clearly one of the 'classiest' hotels in the city, with a Michelin-starred restaurant) is a 10 minute walk from the nearest beach. Turning right when you reach it will take you fairly quickly to Port Olimpic (which I've referred to in previous posts). Turning left will take you to more beaches. The hotel is less than 5 minutes walk from Poblenou Metro station, where a Line 4 Metro train will take you very quickly to Jaume I Metro station, which is at the heart of the old city and within easy walking distance of La Rambla (or you can stay on until Passeig de Gràcia and take a Line 3 train to any of the three Metro stations along La Rambla).
It looks very expensive to me (although I've not actually checked any prices) but, as you're only there for three days, it might be worth splashing out a bit. The hotels own website guarantees to offer the lowest rates (although I'd still check elsewhere) and gives you €20 spending money per day as well if you join the hotel group's loyalty scheme:
http://www.melia.com/en/hotels/spain/barcelona/melia-barcelona-sky/index.html
Like the Melià Barcelona Sky, the Vincci Bit is part of big luxury hotel group, so it's likely to be pricey. (They are both the type of places where rich people hold their wedding receptions or major companies host their conferences. Don't expect low prices!). The hotel's own website also promises to offer the best rates:
http://www.vinccihoteles.com/eng/Hotels/Spain/Barcelona/Vincci-Bit
However it's a bit further out and you'd have to use either Besòs Mar or Selva de Mar Metro stations. It's also at the far end of the beaches so, on arriving at the seafront you could only turn right (and it's a longer walk to Port Olimpico).
The Melià Barcelona Sky looks better located to me.