The difference between an A3/B3 10W40 and an A3/B4 is actually quite a lot.
First off, the 8 vs 10 TBN thing is the most visible difference but in reality it's probably the least significant. The imposition of higher TBN was politically driven to differentiate these oils from Low SAPs oils.
To meet both the ACEA B3 & B4 specs, engine oils must be put through their paces on the 60 hour VW TDI diesel test. Without getting overly technical, a B4 oil must leave the pistons cleaner with less ring stick. To achieve this, you generally need to put more Ashless Dispersant in a B4 oil.
Now all things being equal, putting more Ashless in an oil, increases it's Noack volatility. The 72 hour Peugeot TU5 test that you need to pass for ACEA A3 doesn't like high Noack. So a B4 oil, with higher levels of ashless, typically needs more synthetic base oil in the mix to bring the Noack back to something that is acceptable to the TU5. This extra synthetic directionally reduces VII loading (which is a good thing).
So, relative to an A3/B3 oil, an A3/B4 10W40 will contain...
...more metallic detergent (for TBN)
...more ashless dispersant (for Tdi)
...more Group III (for TU5)
...less VII polymer
Although much of this primarily manifests itself as better performance in diesel engines (with no PDFs), the oil will also be better for gasoline engines.
However, expect the A3/B4 10W40 to cost more..
I was trying to find an HM oil that is not too far off from BMW's LL01 spec. The LL01 spec uses ACEA A3/B4 as baseline. But if you don't run very long OCI, it probably does not matter much.
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