Yes, there are – though the number of candidates differs quite a bit depending on the exact definition of your question.
Aspiration only
If you focus exclusively on aspiration, then a great number of Germanic languages, including English, have such a distinction.
In English (primarily European, as the question is about Europe, but also American and Antipodean), the contrast between /b/ and /p/ in initial position (i.e., at the very beginning of a stress unit, which is where the contrast is strongest) is primarily one of aspiration: /b/ is unaspirated, /p/ is aspirated.
Very often, /b/ is also voiced, but this is far less consistent than the aspiration of /p/. It’s not at all uncommon for a word like ban to be phonetically [paˑn] rather than [baˑn], but pronouncing pan as [paˑn] instead of [pʰaˑn] would almost certainly result in the listener hearing ban instead of pan, as very clearly demonstrated by Geoff Lindsey in Speech is really SBEECH on YouTube.
This tendency is even more pronounced in other Germanic languages like German, Icelandic and Danish where there’s less variation in whether or not /b/ is voiced.
The situation in German is somewhat complicated depending on dialect, but at least in many dialects the /b/ vs /p/ distinction is between primarily voiceless unaspirated [b̥] and primarily aspirated [pʰ].
Things are more straightforward in Icelandic, where the contrast is between [p] and [pʰ] (i.e., both are fortis and aspiration is the only distinguishing feature).
In Danish, both /b/ and /p/ are traditionally described as lenis and unvoiced, i.e., [b̥] and [b̥ʰ], though they’re often denoted [p] and [pʰ] for ease, since there is no lenis–fortis distinction.
Apart from these Germanic languages, the same type of aspiration-based distinction is also found in the extant Celtic languages, such as Scottish Gaelic (and to a lesser degree also in Irish Gaelic, though the unaspirated stops are often voiced in Irish – the situation there is similar to English) and Welsh (also similar to English). Breton is the only one where voicing is truly the main distinguishing feature, probably due to French influence.
Aspiration + voicing
All that is taking your question very literally: it’s the same distinction as Classical Greek π [p] vs φ [pʰ], leaving aside the rest of the phonemic inventory.
What it fails to take into account is that Greek additionally had a fully voiced counterpart β [b]. None of the Germanic or Gaelic languages have that. In fact, finding indigenous European languages that possess this feature is quite hard – I obviously don’t have intimate knowledge of all languages spoken in Europe, but I can only think of very few modern-day candidates that fit the bill, and they’re all located around the very edges of Europe (and apart from Armenian, they’re also all non-Indo-European languages).
Classical Armenian had a three-way distinction just like Classical Greek. Modern Western Armenian only has /b/ and /pʰ/ (a situation that rather bizarrely came about not through a simple merger of /p/ and /pʰ/, but by first merging /b/ and /pʰ/ and then subsequently voicing /p/ to /b/), but Eastern Armenian has retained all three.
Georgian almost fits: it has a three-way distinction which includes aspiration, but there is no plain /p/; instead, there is a voiced /b/, a voiceless aspirated /pʰ/ and an ejective /pʼ/, so aspiration isn’t the only distinguishing feature.
But some of the Sámi languages, like North Sámi, do seem to retain a fully ‘compliant’ /b ~ p ~ pʰ/ distinction (others, like Skolt Sámi only have a two-way distinction, usually voiced–unvoiced).
There may be more, but these are the only ones I can think of off the top of my head.
