Trouble update 2.0.10 –> 2.1.3

I have my blogs running on 2.0.10 – one very small one (used for testing) and one bigger. Both running on MySQL 4.1.14.
I have upgraded the small one to 2.1.3 without a problem, and I can do everything I want (well, almost).
The other one can be upgraded to 2.1.3 – it will run without a problem, but access to the administrator page shows “Need to upgrade”and the I get:

Fatal error: Allowed memory size of 8388608 bytes exhausted (tried to allocate 4 bytes) in /sysblog/wp-admin/upgrade-schema.php on line 134

Fatal error: Allowed memory size of 8388608 bytes exhausted (tried to allocate 5408 bytes) in /sysblog/wp-includes/cache.php on line 444

The numbers anmd locations differ. There seems to be no way to get around the problem so I reversed the installation (returned to 2.0.10).

What’s wrong? The weird part is that the smaller blog (just a few possts) can be upgraded but the other one won’t – even when less than 100 posts!