Archaeology reading Vs Southampton

For a niche subject like Archaeology it isnt going to make much difference.
If you prefer the course at Reading, go with it.

It wont.
Many people on TSR get fixated on this, and really its something that only school-leavers obsess about.
For Archaeology its irrelevant - any jobs you get within that field will be because of the specialisms/interests that you developed within your degree and the work-experience and field work you did, not 'which Uni'.

For example, one of my friends got to do fieldwork in a certain, which has led to a job there etc, and wouldn't have gotten it otherwise.

Yes, but they wouldn't have known that in advance of picking that Uni as a Firm choice would they.

A lot of universities advertise and clearly state where students can go on digs. Just something to take into consideration.

All Archaeology courses include practical fieldwork.

I know that, as I studied it myself. I am just pointing out that, if a student is interested in working in particular places, it is useful to look at where a university sends its students for practical fieldwork.