The difference between common-law and conjugal is this: basically, a couple qualifies as common-law partners when they can demonstrate that they have lived together, in a marriage-like relationship, for at least a continuous year. Conjugal partner qualification is about qualifying as common-law partners without having lived together for at least a year because of fear of persecution due to the relationship, or an immigration barrier that prevents the couple from living together in either country for long enough to establish a common-law relationship. There must also be an impediment to marriage, in other words, a couple can't just decide they'd rather not marry - when they could legally do that - in favour of being common-law partners when they can't meet that definition . . . and then expect to qualify as conjugal partners instead. The conjugal partner class is there to make exceptions, when warranted, to the common-law qualification - in order not to discriminate against genuine couples who cannot "legally" find a way to be together.
The primary concern you should have at this point is making sure that you don't back yourself into a corner by not declaring your relationship to him when you file for PR - thus excluding him from being able to be sponsored by you in the future. This is a sticky situation because there are the issues of no divorce in the Philippines (so you can't marry) and the fact that you are unable to live together because he's there and you're here . . . but you do live together when you go home, and it appears that your own minds and hearts it is a relationship with intention of permanence. So, if you didn't include him, CIC could say that you were in a "qualifying relationship" with him and you purposely didn't disclose the relationship out of fear that it would complicate your own PR status - and they would bar you from applying to sponsor him in the future. On the other hand, adding him to your application now will complicate it because you will have to demonstrate that, without having lived together for a year and without benefit of marriage, your relationship still meets the criteria that qualifies him as an applicant in the conjugal partner class. In other words, when it suits CIC, they will make you prove he qualifies as a conjugal partner (when you add him to your own PR application), but if you were to leave him off and then apply to sponsor him at a later date, they'd likely refuse the application because you didn't declare him originally, and you'd find yourself in the position of having to appeal and prove he didn't qualify as a conjugal partner! So my advice would be: include him on your application for PR as an accompanying conjugal partner. Of course, adding a partner to your application - especially one living overseas - will complicate the application, but in your situation I think it's the safest option. You will need to be able to demonstrate that you have had a genuine, ongoing relationship . . . the lack of marriage (because of the customs surrounding divorce in the Philippines) shouldn't be a huge issue. So conjugal could "fly" for the two of you - you have the required impediment to marriage and restrictions on being together because of an immigration issue . . . however, the possible "catch" might be that you are not Canadian - so, consequently, they could say that there isn't an immigration barrier because you could choose to go home and live with him in the Philippines and establish a qualifying common-law relationship. Whether they'd go there or not is anybody's guess.
Regardless, it's important that you keep all records of your communications - phone calls, texts, chats, letters, etc., and all proof of your visits to the Philippines and time spent with him there . . . especially photos. I'd also suggest that he make at least a couple of attempts at a TRV to come visit you - even though he will most likely be refused. It's important that you establish evidence of your desire and attempts to be together - and demonstrate that you were refused that opportunity by immigration barriers.