Hello Robbo2,
Not too clear about the type of backpacking you're meaning, and from my angle an extended solo wander around urban areas will give a different answer to an extended wander around a wilderness area.
For an urbanised trip I may well cast off alone, but think I'd prefer a compatible companion for part of the time, particularly if you do not know the language. It's nice to have someone to discuss things with and depending on locations of course, it could also be handy to have a companion - there are spots in most cities where the inhabitants make grizzlies look like pussycats!
However, the main reason even though it's a bit of an anomaly, is that I always feel far lonelier wandering around alone in a crowded city than I ever feel when completely remote from my species in the wilderness. But if it's a 'backcountry' trip you have in mind, my preference is going solo. Here's why..

1. You can move at your own pace.
2. You always get the best spot for your tent - and can
often stop in excellent locations where there is only a suitable
tent site for one.
3. You see much more wildlife when alone.
4. More satisfaction out of being as self reliant as possible.
5. Nice to be able to let your thoughts wander where they
will without having to react to anyone.
5. Being completely alone for extended periods makes me
appreciate friends and folk when a trip is over.

Maybe the answer for either scenario is to consider starting off solo - you can likely team up with someone at a later date if you wish but if you commit yourself with someone from the start you may be unfortunate to find you are not compatible or that you'd just rather have some solo time out there.