Percatar(se)

[JPablo]

2. prnl. Darse cuenta clara de algo, tomar conciencia de ello. No se percató de su error.

It is a very close synonym. The word "percatarse" has the added connotation of "clear realization". It is used normally at a higher register, and philosophical writings. ¿Te das cuenta de la diferencia?
¿Te percatas de la diferencia?

¿Te das perfecta cuenta de la diferencia?
In the 3 questions I am asking "Do you realize the difference?"
There is a nuance of difference, but it is subtle.
I will commonly use "darme/te/se cuenta de" rather than "percatarme/te/se". (It sounds a bit highbrow to me... so I tend to agree with Poli on that.)

In a colloquial/ironic/sarcastic level one could ask (sounding purposely pedantic)

¿Te percatas de la indirecta? (As in, "Do you get the hint?")

When I made an error before, I would say,

No me di cuenta de mi error.
To say,
Perdón, no me percaté de mi error, while it is fine and understandable, it sounds a bit "affected" to me.

[laepelba]

From what I read about percatarse, it is more like the English "perceive" and darse cuenta is more like the English "realize"... I got the impression that "percatarse" is at a deeper mental level than "darse cuenta"...

For example:
- Me di cuenta de dejé mi bolso en el omnibus. (It hit me that ... DOH ... I left my purse on the bus....)
- Me percaté que había tensión racial en mi clase. (When a certain occurrence happened in my classroom, I had a deeper perception of the racial tensions that existed between my students...)

Or no?

[JPablo]

Originally Posted by laepelba

From what I read about percatarse, it is more like the English "perceive" and darse cuenta is more like the English "realize"... I got the impression that "percatarse" is at a deeper mental level than "darse cuenta"...

For example:
- Me di cuenta de que dejé mi bolso en el omnibus. (It hit me that ... DOH ... I left my purse on the bus....)
- Me percaté de que había tensión racial en mi clase. (When a certain occurrence happened in my classroom, I had a deeper perception of the racial tensions that existed between my students...)

Or no?

Sí. That is correct to some extent. In these examples, using "percatarse" in the first example, (which wouldn't be "incorrect") it would sound ridiculously pedantic.

In the second example, (for all practical purposes) in my opinion you could use both expressions with almost the same conceptual understanding. Yes, granting that "percatarse" implies or may imply a deeper understanding than "darse cuenta".
But you can see in DRAE, they use "percatarse" to define "darse cuenta",
darse cuenta de algo. 1. loc. verb. Advertirlo, percatarse de ello.
2. loc. verb. coloq. Comprenderlo, entenderlo.

I believe you are going to have to play with every context to see the implied meaning and/or the stress on one nuance or another, but your perception of these words/expressions seems "on the rails".

I include here Moliner too, (usage definitions) given that its definition matches with your perception, (the bolded parts is done by me)

percatarse (de «per-1» y «catar», mirar) prnl. Adquirir conocimiento reflexivo de cierta cosa: ‘No se ha percatado de lo que le has dicho. Es necesario que te percates de la importancia del hecho’. Darse cuenta. Percibir una cosa no patente o no hecha para que sea percibida: ‘¿No te has percatado de que tenían ganas de que nos fuéramos?’. Notar.

Catálogo [related expressions, I am not including all of them]
advertir, apercibirse, caer en, captar, coger, tomar conciencia, concienciarse, coscarse, caer en la cuenta, darse cuenta, dar en, descubrir, despertar, diquelar, echar de ver, enterarse, no escaparse, fijarse, filar, hallar, tomar nota, notar, coger [o captar] la onda, observar

Caer en la cuenta. Percatarse de pronto de algo que no se comprendía, no se sabía o no se había notado: ‘No caí en la cuenta de quién era hasta que me habló de ti. Entonces caí en la cuenta de por qué no había querido venir’.

[poli]

What a lot of very good information. JP. I have often wondered how to say get the hint, but always forget to bring it up. Me percato la indirecta.

[JPablo]

Originally Posted by poli

What a lot of very good information. JP. I have often wondered how to say get the hint, but always forget to bring it up. Me percato de la indirecta.

Well, there you have it. But it is always used with "de"

In Panhispánico de Dudas you have,
percatarse. ‘Darse cuenta de algo’. Rige un complemento con de: «Jean Leroy se percató de que le temblaban las manos» (Montero Trenza [Cuba 1987]). Debe evitarse, en el habla esmerada, omitir la preposición (→ queísmo, 1a): Se percató que...

(I forgot to mention the "queísmo" to Lou Ann, but there it is too!)