During a long business trip, I've spent 4 consecutive months in the Avari and 1 month in the Pearl Continental. Here I compare the two.

In one word : if you want a friendly, quiet hotel (especially for long stays), go to the Avari ; if you favor larger, more modern rooms and facilities, go the the Pearl Continental.
The Pearl Continental is a larger, more recent hotel with overall better facilities (except the internet connection) ; the Avari is a bit old-fashioned but quieter, less crowded and has a friendlier staff. Prices are similar (~$130 on a corporate rate).

Overall atmosphere: the Avari is a mid-size (3 floors) 1980'-style hotel ; the PC (recently renovated) is a 9-floor hotel with a huge lobby. The PC is constantly crowded, as it mainly serves as a place for conferences, marriages or any social events for the Lahore high society (especially on week-ends, where its restaurants are crowded). Only 10% to 20% of people in the PC lobby are actually hotel guests. The Avari also hosts events, but it's much smaller and considered less fashionable by Lahoris, so it's much quieter.

Rooms: PC rooms are better, especially in the new wing : larger, modern, with an excellent bathroom. If you have large amount of luggage, they are more convenient (although the Avari's will make do though). The Avari rooms aren't as good, not quite 5-star quality.

Service: Avari service is much better. Due to the much smaller number of people wandering in the hotel, the Avari staff can afford to spend more time with hotel guests ; there are also overall friendlier and extremely helpful.

Quality of sleep: both hotels are far from the street, and anyway in Pakistan nobody opens windows. None of the hotels has truly sound-proof walls. During my stay the Avari had maintenance works 2-3 times.

Restaurants: both the Avari and PC offer Pakistani (buffet or à la carte), Chinese and Japanese restaurants (plus an Italian one in the PC). Overall quality is similar, except for the Avari Japanese (Fujiyama) which has a authentic Japanese menu (not at all the case in the PC). Neither Chinese restaurants are authentic. Restaurants are quite expensive in both places, especially the Avari (where standard buffet is 15 dollars).

Internet: the Avari has the internet offer you'd expect in any business hotel today (free, wi-fi everywhere, no login) ; the PC has (at least in Oct. 2011) an awful pay-by-the hour / day system, in which you have to order paper vouchers from the reception. It's expensive and extremely annoying. As I was staying a long time, I ended up having a permanent internet connection though, so you may try to ask for it. Internet speed is pretty slow in both hotels (do not expect to receive a 4-mb attachement in seconds).

Lounges: the Avari lounges are OK, but the top-floor executive lounge at the PC has better food and a very nice view.

Business center : much better in the PC for if you need computer access and printing.

Conference rooms: a larger number in the PC. In the Avari, two 10-seat + one 20-seat. Sometimes can be crowded. In the Avari, for a longer stay, you can ask to convert one room in a business room and use it permanently for a reasonable fee.

Gym & pool: much better in the PC : modern equipement (although the gym is still small compared with international standards). Old, almost non-functionnal stuff in the Avari. Pool is nicer in the Avari, yet is situated just next to the large windows of the Japanese restaurant where diners have a clear view on the pool, which might by annoying.

Shops: larger number of shops in the PC (overpriced, of course).

Cars: same convenient Hertz renting system (usually you book a car with chauffeur) in both hotels, although the PC booking system is a bit faster.

Alcohol (foreigners only) : large bar at the PC ; much smaller in the Avari. Did not try the drinks myself, but in both hotels they seemed quite expensive with limited choice.

Security: Avari & PC security level is considered equivalent by international organisations. Anyway, if you're a foreigner not used to traveling to risky countries, the amount of security can be quite scary on your first days (the PC definitely feels like a bunker). Don't worry though ! Northern Punjab is quite safe and even as foreigner you can walk alone safely in most of streets in Lahore (especially if you dress the local way), and Pakistani are extremely friendly !