For the most part, yes. It was $200 cheaper and had more appealing exclusives in the opinion of many during its first few years. That's not to mention how much Xbox Live took off.
I mean, we are talking about the system that competed against the successor to the PS2.... the PS2. It couldn't have ate into that success simply due to releasing first and nothing more -- especially given the position the Xbox brand was in before 2006.
But it wasnt nothing more.
Both of what you mentioned came with time. Time gained from launching signifcantly earlier. 2005 xbox live was little better than 2001 Xbox live, it was only with the investment both on Microsofts end and via people buying into the platform (as well as Sonys lack of investment) that the thing grew so quickly. Likewise, the more appealing exclusives are also a product of time and more mature Dev tools.
A launch Gears of war would not of had the impact the game did releasing a year later with the correct time in the oven. Meanwhile Sony and its partners were struggling with launch hardware that was already harder to develop for. If say Gears in its release state, went up against Uncharted in its release state, (they both released the following november after their respective platform launch) there would be much more debate between gamers about what platform had the better exclusives.
This time both are are on a much more equal footing. Xbox one live does like it still has an edge, but until both consoles launch, its unknown how much of one it has. Likewise, the development tools of both consoles are a much closer in maturity so you will be seeing some of the best games of the platform far faster, especailly as Sony has far more experienced studios under their belt.
Finally, we need to move away from this Successor talk. One platform does not predict the performance of its successor. The Xbox didnt predict the 360, The Wii Hasnt predicted the WiiU, The PS2 didnt the PS3. What they can predict is the company philosophy going into the start of the generation, which for many in the short term favours Sony over Microsoft, even if you consider Microsoft to have the stronger launch lineup.
Sony has made it quite clear that they have built a system for developers to deliver high quailty experiences to willing gamers. Microsoft have made it quite clear they want a console balanced around delivery of all media.
It seems clear to me that Sony has the edge now, but microsoft has the potential to decimate in the casual market. However, from a gaming point of view, Sonys approach may lead to a much higher intial install base which in turn will lead to higher quailty games, both from first and third party. Im not predicting a runaway success because neither are at mass market price points, but The design philosophy of the PS4 means in the short term I very much doubt microsoft will have the success they would like. Once they get the causals on board, its another race entirely but disrehgarding Sonys power advantage even then is foolhardy in my opinion.