I think the confusion, here and on the previous question regarding degrees of comparison, stems from conflating syntactical and semantic approaches.
Syntax focuses on structural relationships. In syntax, something is called adjectival if it modifies a noun. That modification can be either attributively (within the noun phrase) or predicatively (in a different phrase linked by a verbal). So, speaking syntactically, lots of things can function adjectivally: single words, prepositional phrases, relative clauses, participles, etc.
Semantics focuses on meaning. Here we are still concerned with modifying nouns, but we are particularly concerned with distinguishing qualitatively among different types of qualification. What sorts of assertions do different modifiers imply? Different taxonomies are possible, but the one most relevant is classification by temporal or dynamic force.
One class of modifiers ascribes some quality or attribute to a noun. This quality is asserted generally, in a way that lacks temporal force. For example, if we were to state the assertion implicit in "the tall man" (vir longus) in the form of a complete sentence, we could do so only with a stative verb: "The man is tall" (vir longus est).
But we can do some other things with a modifier of this sort. For one thing, qualities usually have the property of scale, meaning that the attribution can be qualified in terms of degree. We can say "the very tall man" (vir praelongus / longissimus), or "the not very tall at all man" (vir haud longus). Precisely because the assertion can be scaled, it can also be compared: "a man taller than Mark" (vir Marco longior). This kind of modifier I would call an adjective.
Now, let's look another type of modifier: "a running soldier" (miles currens). What's different here? The modifier is not ascribing to the noun a quality but rather positing that the noun is engaged in a certain activity at a certain time. When we state the implied assertion as a sentence, we get a non-stative verb: "A soldier is (currently*) running" (miles [nunc*] currit). Actions, unlike qualities, do not possess the property of scale, as we cannot say "a very running soldier" (miles currentissimus), and consequently we cannot compare these assertions -- "a more running soldier" or "a runningier soldier" (miles currentior) without adding an adverb specifying with respect to what the comparison is being made, e.g., : "a soldier running more often than Mark runs" (miles Marco crebrius currens). This is a participle-qua-verbal being used, syntactically speaking, adjectivally.
If transitive, this kind of modifier can take a direct object. The assertion implied in "The centurion drinking wine" (centurio vinum bibens) is "The centurion is (currently) drinking wine" (centurio vinum [nunc] bibit). In both English and Latin, this kind of adjectival use is equivalent to a relative clause: "The centurion who is (currently) drinking wine" (centurio qui vinum [nunc] bibit). And again, the action doesn't possess scale: not "the centurion very drinking wine" (centurio vinum bibentissimus) but "the centurion drinking a lot of wine" (centurio multum vinum bibens). And it doesn't compare: not "the centurion more drinking wine than Mark" (centurio Marco vinum bibentior) but "the centurion drinking more wine than Mark" (centurio bibens plus vini quam Marcus).
[Note: The same situation holds for participles functioning as the heads of adverbial clauses, which is probably the majority of participles, at least in the nominative.]
Now, let's look at one final category, using the example "a loving wife" (uxor amans). In both English and Latin, it's clear that the modifier is derived from a verb. The words have the morphology of participles. The semantic question remains, what is being asserted about the noun? In English, it's clear even apart from other context that "loving" is attributing a quality or perhaps a kind of habitual activity; it is not positing an action at a definite time. It can be rephrased "a wife who behaves in a generally loving way," but not "a wife who is currently engaged in loving." Like other qualities, it scales: "a very loving wife." It compares: "a wife more loving than Mark's"). This is a participle-qua-adjective.
Now, in Latin, we would need more context to determine whether the participle is attributing a quality (participle-qua-adjective) or positing an action (participle-qua-verbal). But if it's acting as a mere adjective, it will behave like other adjectives. It will scale (amantissima) and compare (amantior quam Marci uxor).
It can even be used substantively, becoming a noun. In such cases, it can take an oblique object: amantes patriae = nation-lovers. The important thing to note here is that such a usage still ascribes a general quality, it doesn't posit an activity with definite temporal force: "people who love the nation", not "people who are right now loving the nation."
So, I hope that clears things up. There are (for the purposes of this discussion) two kinds of modifiers, those that attribute qualities and those that posit actions. Qualities possess scale, so they can take comparison; actions possess dynamic, temporal force, so they can take objects. Participles can perform either task, so in the positive degree rely on context for interpretation.
- When I use "currently" (nunc) to express temporal force, the time should really be understood relatively in terms of the reference frame, not absolutely. E.g., Caesar viderat militem currentem = "Caesar had seen a running man" = "Caesar had seen a man who was running at the time Caesar saw him".