They ordered one slightly later than the UK and the US (let's ignore Israel which is basically a large scale trial). The main difference: the EU used normal certification processes, just sped them up considerably. The UK and US used emergncy certification.
The volumes the EU ordered initially were absolutely sufficient with 4+ doses per EU inhabitant. Manufacturing capacities were sufficient for that as well. It all started to go south as soon as memeber states looked for scape goats why vaccination happened so slowly. First the manufacturers, then the EU, then the federal government (where applicable). It is a last-mile distribution issue if you will now, not a manufacturing one.
I think that's a very charitable interpretation of events. Realistically the EU negotiated on behalf of the 27 member countries to try to get the best deal on price, and perhaps more importantly, to avoid the inevitable tensions which would follow from one member country securing more than another member country. This process slowed down the negotiation process.
Whether there is any truth in the EUs certification being conducted differently is a bit moot given they have approved the same vaccines based on the same trial data.
I don't think it is charitable. The EU had to juggle 27 individual countries, one central certification and Brexit. They had to avoid a situation in which rich countries, e.g. Germany, outbids poorer countries, e.g. Hungary or Greee. They managed to do that. They over purchased, they split orders betwen suppliers thus further minimizing the risk.
And they did all that using normal certification. They even pointed out, quite clearly, that the actual managemen of vaccination campaigns, the vaccine ordering and the national distribution is up to the member states.
The last part shows very different results, e.g. in germany Mecklenburg-Vorpommern is far ahead in per capita vaccines. Bavaria for example is behind them. All we won with focusing on the supply of vaccines so far in a shutdown of Pfizer's pant in Belgium to produce more doses, which are not needed, at a later point of time. And a nasty contract dipute with AZ after the media and, at least IMHO, politians singled out AZ as a scape goat.
The volumes the EU ordered initially were absolutely sufficient with 4+ doses per EU inhabitant. Manufacturing capacities were sufficient for that as well. It all started to go south as soon as memeber states looked for scape goats why vaccination happened so slowly. First the manufacturers, then the EU, then the federal government (where applicable). It is a last-mile distribution issue if you will now, not a manufacturing one.